A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...

Can someone explain how to get equation 27.14 below? I understand the first usage of Ito's Lemma to get $d(\ln f-\ln g)$ but I do not understand how to use Ito's Lemma to go from $d(\ln \frac{f}{g})$ ...

What is the difference between a random process that is adapted to a filteration and one that had the martingale property. It seems the two notions are quite similar and would be helpful to construct ...

The simply put question is as follows: do we need to restrict ourselves to EMM exclusively when pricing European contingent claims (=option payoffs) even if markets are incomplete?
In particular, a ...

I was reading the papers co-authored by Harrison, Kreps and Pliska, that initiated the formal research on the connection between pricing, martingale measures, arbitrage and completeness. I have some ...

Assuming I have a dividend paying asset $S$ with dividend process $D$. Now I would like to use the bank account process $B$ as numeraire and determine the dynamics of $S$ under the the corresponding ...

Do you have any idea about how we can prove, and under which conditions, that an equivalent martingale measure (EMM) in an incomplete market is unique? The assumptions we have made are:
1) that the ...

Quantitative finance formular are mostly based on martingales, Poisson jump, GBM, CEV, etc..
The logic behind it is that martingale means the future could not be predicted, or, EMH (Efficient-market ...

I'm working through different books about financial mathematics and solving some problems I get stuck.
Suppose you define an arbitrary stochastic process, for example
$ X_t := W_t^8-8t $ where $ W_t ...

I'm studying for an exam in financial models and came across this question:
"An agent with $C^2$ strictly increasing concave utility $U$ has wealth $w_0$ at time 0, and wishes to invest his wealth in ...